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<TITLE>CLN, a Class Library for Numbers - 11. Using the library</TITLE></HEAD><BODY>Go to the <A HREF="cln_1.html">first</A>, <A HREF="cln_10.html">previous</A>, <A HREF="cln_12.html">next</A>, <A HREF="cln_13.html">last</A> section, <A HREF="cln_toc.html">table of contents</A>.<P><HR><P>
<H1><A NAME="SEC64" HREF="cln_toc.html#TOC64">11. Using the library</A></H1>
<P>For the following discussion, we will assume that you have installedthe CLN source in <CODE>$CLN_DIR</CODE> and built it in <CODE>$CLN_TARGETDIR</CODE>.For example, for me it's <CODE>CLN_DIR="$HOME/cln"</CODE> and<CODE>CLN_TARGETDIR="$HOME/cln/linuxelf"</CODE>. You might define these asenvironment variables, or directly substitute the appropriate values.
<H2><A NAME="SEC65" HREF="cln_toc.html#TOC65">11.1 Compiler options</A></H2><P><A NAME="IDX320"></A>
<P>Until you have installed CLN in a public place, the following options areneeded:
<P>When you compile CLN application code, add the flags
<PRE> -I$CLN_DIR/include -I$CLN_TARGETDIR/include</PRE>
<P>to the C++ compiler's command line (<CODE>make</CODE> variable CFLAGS or CXXFLAGS).When you link CLN application code to form an executable, add the flags
<PRE> $CLN_TARGETDIR/src/libcln.a</PRE>
<P>to the C/C++ compiler's command line (<CODE>make</CODE> variable LIBS).
<P>If you did a <CODE>make install</CODE>, the include files are installed in apublic directory (normally <CODE>/usr/local/include</CODE>), hence you don'tneed special flags for compiling. The library has been installed to apublic directory as well (normally <CODE>/usr/local/lib</CODE>), hence whenlinking a CLN application it is sufficient to give the flag <CODE>-lcln</CODE>.
<H2><A NAME="SEC66" HREF="cln_toc.html#TOC66">11.2 Include files</A></H2><P><A NAME="IDX321"></A><A NAME="IDX322"></A>
<P>Here is a summary of the include files and their contents.
<DL COMPACT>
<DT><CODE><cl_object.h></CODE><DD>General definitions, reference counting, garbage collection.<DT><CODE><cl_number.h></CODE><DD>The class cl_number.<DT><CODE><cl_complex.h></CODE><DD>Functions for class cl_N, the complex numbers.<DT><CODE><cl_real.h></CODE><DD>Functions for class cl_R, the real numbers.<DT><CODE><cl_float.h></CODE><DD>Functions for class cl_F, the floats.<DT><CODE><cl_sfloat.h></CODE><DD>Functions for class cl_SF, the short-floats.<DT><CODE><cl_ffloat.h></CODE><DD>Functions for class cl_FF, the single-floats.<DT><CODE><cl_dfloat.h></CODE><DD>Functions for class cl_DF, the double-floats.<DT><CODE><cl_lfloat.h></CODE><DD>Functions for class cl_LF, the long-floats.<DT><CODE><cl_rational.h></CODE><DD>Functions for class cl_RA, the rational numbers.<DT><CODE><cl_integer.h></CODE><DD>Functions for class cl_I, the integers.<DT><CODE><cl_io.h></CODE><DD>Input/Output.<DT><CODE><cl_complex_io.h></CODE><DD>Input/Output for class cl_N, the complex numbers.<DT><CODE><cl_real_io.h></CODE><DD>Input/Output for class cl_R, the real numbers.<DT><CODE><cl_float_io.h></CODE><DD>Input/Output for class cl_F, the floats.<DT><CODE><cl_sfloat_io.h></CODE><DD>Input/Output for class cl_SF, the short-floats.<DT><CODE><cl_ffloat_io.h></CODE><DD>Input/Output for class cl_FF, the single-floats.<DT><CODE><cl_dfloat_io.h></CODE><DD>Input/Output for class cl_DF, the double-floats.<DT><CODE><cl_lfloat_io.h></CODE><DD>Input/Output for class cl_LF, the long-floats.<DT><CODE><cl_rational_io.h></CODE><DD>Input/Output for class cl_RA, the rational numbers.<DT><CODE><cl_integer_io.h></CODE><DD>Input/Output for class cl_I, the integers.<DT><CODE><cl_input.h></CODE><DD>Flags for customizing input operations.<DT><CODE><cl_output.h></CODE><DD>Flags for customizing output operations.<DT><CODE><cl_malloc.h></CODE><DD><CODE>cl_malloc_hook</CODE>, <CODE>cl_free_hook</CODE>.<DT><CODE><cl_abort.h></CODE><DD><CODE>cl_abort</CODE>.<DT><CODE><cl_condition.h></CODE><DD>Conditions/exceptions.<DT><CODE><cl_string.h></CODE><DD>Strings.<DT><CODE><cl_symbol.h></CODE><DD>Symbols.<DT><CODE><cl_proplist.h></CODE><DD>Property lists.<DT><CODE><cl_ring.h></CODE><DD>General rings.<DT><CODE><cl_null_ring.h></CODE><DD>The null ring.<DT><CODE><cl_complex_ring.h></CODE><DD>The ring of complex numbers.<DT><CODE><cl_real_ring.h></CODE><DD>The ring of real numbers.<DT><CODE><cl_rational_ring.h></CODE><DD>The ring of rational numbers.<DT><CODE><cl_integer_ring.h></CODE><DD>The ring of integers.<DT><CODE><cl_numtheory.h></CODE><DD>Number threory functions.<DT><CODE><cl_modinteger.h></CODE><DD>Modular integers.<DT><CODE><cl_V.h></CODE><DD>Vectors.<DT><CODE><cl_GV.h></CODE><DD>General vectors.<DT><CODE><cl_GV_number.h></CODE><DD>General vectors over cl_number.<DT><CODE><cl_GV_complex.h></CODE><DD>General vectors over cl_N.<DT><CODE><cl_GV_real.h></CODE><DD>General vectors over cl_R.<DT><CODE><cl_GV_rational.h></CODE><DD>General vectors over cl_RA.<DT><CODE><cl_GV_integer.h></CODE><DD>General vectors over cl_I.<DT><CODE><cl_GV_modinteger.h></CODE><DD>General vectors of modular integers.<DT><CODE><cl_SV.h></CODE><DD>Simple vectors.<DT><CODE><cl_SV_number.h></CODE><DD>Simple vectors over cl_number.<DT><CODE><cl_SV_complex.h></CODE><DD>Simple vectors over cl_N.<DT><CODE><cl_SV_real.h></CODE><DD>Simple vectors over cl_R.<DT><CODE><cl_SV_rational.h></CODE><DD>Simple vectors over cl_RA.<DT><CODE><cl_SV_integer.h></CODE><DD>Simple vectors over cl_I.<DT><CODE><cl_SV_ringelt.h></CODE><DD>Simple vectors of general ring elements.<DT><CODE><cl_univpoly.h></CODE><DD>Univariate polynomials.<DT><CODE><cl_univpoly_integer.h></CODE><DD>Univariate polynomials over the integers.<DT><CODE><cl_univpoly_rational.h></CODE><DD>Univariate polynomials over the rational numbers.<DT><CODE><cl_univpoly_real.h></CODE><DD>Univariate polynomials over the real numbers.<DT><CODE><cl_univpoly_complex.h></CODE><DD>Univariate polynomials over the complex numbers.<DT><CODE><cl_univpoly_modint.h></CODE><DD>Univariate polynomials over modular integer rings.<DT><CODE><cl_timing.h></CODE><DD>Timing facilities.<DT><CODE><cln.h></CODE><DD>Includes all of the above.</DL>
<H2><A NAME="SEC67" HREF="cln_toc.html#TOC67">11.3 An Example</A></H2>
<P>A function which computes the nth Fibonacci number can be written as follows.<A NAME="IDX323"></A>
<PRE>#include <cl_integer.h>#include <cl_real.h>
// Returns F_n, computed as the nearest integer to// ((1+sqrt(5))/2)^n/sqrt(5). Assume n>=0.const cl_I fibonacci (int n){ // Need a precision of ((1+sqrt(5))/2)^-n. cl_float_format_t prec = cl_float_format((int)(0.208987641*n+5)); cl_R sqrt5 = sqrt(cl_float(5,prec)); cl_R phi = (1+sqrt5)/2; return round1( expt(phi,n)/sqrt5 );}</PRE>
<P>Let's explain what is going on in detail.
<P>The include file <CODE><cl_integer.h></CODE> is necessary because the type<CODE>cl_I</CODE> is used in the function, and the include file <CODE><cl_real.h></CODE>is needed for the type <CODE>cl_R</CODE> and the floating point number functions.The order of the include files does not matter.
<P>Then comes the function declaration. The argument is an <CODE>int</CODE>, theresult an integer. The return type is defined as <SAMP>`const cl_I'</SAMP>, notsimply <SAMP>`cl_I'</SAMP>, because that allows the compiler to detect typos like<SAMP>`fibonacci(n) = 100'</SAMP>. It would be possible to declare the returntype as <CODE>const cl_R</CODE> (real number) or even <CODE>const cl_N</CODE> (complexnumber). We use the most specialized possible return type because functionswhich call <SAMP>`fibonacci'</SAMP> will be able to profit from the compiler's typeanalysis: Adding two integers is slightly more efficient than adding thesame objects declared as complex numbers, because it needs less typedispatch. Also, when linking to CLN as a non-shared library, this minimizesthe size of the resulting executable program.
<P>The result will be computed as expt(phi,n)/sqrt(5), rounded to the nearestinteger. In order to get a correct result, the absolute error should be lessthan 1/2, i.e. the relative error should be less than sqrt(5)/(2*expt(phi,n)).To this end, the first line computes a floating point precision for sqrt(5)and phi.
<P>Then sqrt(5) is computed by first converting the integer 5 to a floating pointnumber and than taking the square root. The converse, first taking the squareroot of 5, and then converting to the desired precision, would not work inCLN: The square root would be computed to a default precision (normallysingle-float precision), and the following conversion could not help aboutthe lacking accuracy. This is because CLN is not a symbolic computer algebrasystem and does not represent sqrt(5) in a non-numeric way.
<P>The type <CODE>cl_R</CODE> for sqrt5 and, in the following line, phi is the onlypossible choice. You cannot write <CODE>cl_F</CODE> because the C++ compiler canonly infer that <CODE>cl_float(5,prec)</CODE> is a real number. You cannot write<CODE>cl_N</CODE> because a <SAMP>`round1'</SAMP> does not exist for general complexnumbers.
<P>When the function returns, all the local variables in the function areautomatically reclaimed (garbage collected). Only the result survives andgets passed to the caller.
<P>The file <CODE>fibonacci.cc</CODE> in the subdirectory <CODE>examples</CODE>contains this implementation together with an even faster algorithm.
<H2><A NAME="SEC68" HREF="cln_toc.html#TOC68">11.4 Debugging support</A></H2><P><A NAME="IDX324"></A>
<P>When debugging a CLN application with GNU <CODE>gdb</CODE>, two facilities areavailable from the library:
<UL><LI>The library does type checks, range checks, consistency checks at
many places. When one of these fails, the function <CODE>cl_abort()</CODE> iscalled. Its default implementation is to perform an <CODE>exit(1)</CODE>, soyou won't have a core dump. But for debugging, it is best to set abreakpoint at this function:
<PRE>(gdb) break cl_abort</PRE>
When this breakpoint is hit, look at the stack's backtrace:
<PRE>(gdb) where</PRE>
<LI>The debugger's normal <CODE>print</CODE> command doesn't know about
CLN's types and therefore prints mostly useless hexadecimal addresses.CLN offers a function <CODE>cl_print</CODE>, callable from the debugger,for printing number objects. In order to get this function, you haveto define the macro <SAMP>`CL_DEBUG'</SAMP> and then include all the header filesfor which you want <CODE>cl_print</CODE> debugging support. For example:<A NAME="IDX325"></A>
<PRE>#define CL_DEBUG#include <cl_string.h></PRE>
Now, if you have in your program a variable <CODE>cl_string s</CODE>, andinspect it under <CODE>gdb</CODE>, the output may look like this:
<PRE>(gdb) print s$7 = {<cl_gcpointer> = { = {pointer = 0x8055b60, heappointer = 0x8055b60, word = 134568800}}, }(gdb) call cl_print(s)(cl_string) ""$8 = 134568800</PRE>
Note that the output of <CODE>cl_print</CODE> goes to the program's error output,not to gdb's standard output.
Note, however, that the above facility does not work with all CLN types,only with number objects and similar. Therefore CLN offers a member function<CODE>debug_print()</CODE> on all CLN types. The same macro <SAMP>`CL_DEBUG'</SAMP>is needed for this member function to be implemented. Under <CODE>gdb</CODE>,you call it like this:<A NAME="IDX326"></A>
<PRE>(gdb) print s$7 = {<cl_gcpointer> = { = {pointer = 0x8055b60, heappointer = 0x8055b60, word = 134568800}}, }(gdb) call s.debug_print()(cl_string) ""(gdb) define cprint>call ($1).debug_print()>end(gdb) cprint s(cl_string) ""</PRE>
Unfortunately, this feature does not seem to work under all circumstances.</UL>
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